Question

question what is the surface area of the cylinder with height 4 mi and radius 7 mi? round your answer to the nearest thousandth.

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Substitute given values

Given $r = 7$ mi and $h = 4$ mi. First, calculate $2\pi r^2$: $2\pi(7)^2=2\pi\times49 = 98\pi$. Then calculate $2\pi rh$: $2\pi\times7\times4=56\pi$.

Step3: Sum the two parts

$S=98\pi + 56\pi=154\pi$.

Step4: Calculate the numerical value

$S = 154\pi\approx154\times3.14159 = 483.80486\approx483.805$ (rounded to the nearest thousandth).

Answer:

$483.805$ mi²